Noise-induced switching from a symmetry-protected shallow metastable state

Proliferation of unstable states and their impact on stochastic out-of-equilibrium dynamics in two coupled Kerr parametric oscillators

Networks of nonlinear parametric resonators are promising candidates as Ising machines for annealing and optimization. These many-body out-of-equilibrium systems host complex phase diagrams of coexisting stationary states. The plethora of states manifest via a series of bifurcations, including bifurcations that proliferate purely unstable solutions. Here we demonstrate that the latter take a fundamental role in the stochastic dynamics of the system. Specifically, they determine the switching paths and the switching rates between stable solutions. We demonstrate experimentally the impact of the added unstable states on noise-activated switching dynamics in a network of two coupled parametric resonators.

Period Tripling due to Parametric Down-Conversion in Circuit QED

Discrete time-translation symmetry breaking can be observed in periodically driven systems oscillating at a fraction of the frequency of the driving force. However, with the exception of the parametric instability in period doubling, multiperiodic driving does not lead to an instability threshold. In this Letter, we point out that quantum vacuum fluctuations can be generically employed to induce period multiplication. In particular, we discuss the period-tripled states in circuit QED and propose a microwave setup. We show that for weak dissipation or strong driving, the system exhibits a nonequilibrium phase transition in the sense that the timescale over which the period-tripled state is generated can be arbitrarily separated from the timescale of the subsequent dephasing.